This article is cited in 7 papers

Exact Lebesgue Constants for Interpolatory $\mathscr L$-Splines of Third Order

V. A. Kim

Ural State University

Abstract: In this paper, we obtain the Lebesgue constants for interpolatory $\mathscr L$-splines of third order with uniform nodes, i.e., the norms of interpolation operators from $\mathrm C$ to $\mathrm C$ describing the process of interpolation of continuous bounded and continuous periodic functions by $\mathscr L$-splines of third order with uniform nodes on the real line. As a corollary, we obtain exact Lebesgue constants for interpolatory polynomial parabolic splines with uniform nodes.

Keywords: Lebesgue constant, interpolatory $\mathscr L$-spline, $B$-spline, polynomial parabolic spline with uniform nodes, continuous bounded function, continuous periodic function.

UDC: 517.518.8

Received: 26.03.2007

DOI: 10.4213/mzm3865

 English version: Mathematical Notes, 2008, 84:1, 55–63

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